Description

Input

The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5$) — the number of vertices and the number of edges in the graph.

The next $m$ lines contain edges of the graph. The $i$-th line contains the $i$-th edge $x_i, y_i$ ($1 \le x_i, y_i \le n$), where $x_i$ and $y_i$ are vertices connected by the $i$-th edge. The graph can contain loops or multiple edges.

Output

If it is impossible to decompose the given graph into simple cycles, print "NO" in the first line.

Otherwise print "YES" in the first line. In the second line print $k$ — the number of simple cycles in the graph decomposition.

In the next $k$ lines print cycles themselves. The $j$-th line should contain the $j$-th cycle. First, print $c_j$ — the number of vertices in the $j$-th cycle. Then print the cycle as a sequence of vertices. All neighbouring (adjacent) vertices in the printed path should be connected by an edge that isn't contained in other cycles.

6 9
1 2
2 3
1 3
2 4
2 5
4 5
3 5
3 6
5 6

YES
3
4 2 5 4 2 
4 3 6 5 3 
4 1 3 2 1

4 7
1 1
1 2
2 3
3 4
4 1
1 3
1 3

YES
3
2 1 1 
5 1 4 3 2 1 
3 1 3 1

4 8
1 1
1 2
2 3
3 4
4 1
2 4
1 3
1 3

NO

Note

The picture corresponding to the first example: